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An i3-4130 is a performance equivalent of $74 Pentium G4560 and the RX 560 approximates GTX 1050. Some games will have lower fps and more instability in frame rate variation as compared with stronger CPUs, but it is an OK combination. Your issue is where you get the motherboard in 1150 socket. There are $45 basic motherboards for a Pentium G4560 and some have USB 3.1
In the USA, about $200 gets a used mini-tower with quad core i5 2nd or 3rd generation with 8gb ram and a valid Windows 10.
Seeing the whole part list and cost might determine whether the i3 is even worth using.

There is actually no bottleneck on that combination. Your GPU will work perfectly fine with that CPU. However, if you overclock the GPU, then there is a chance that CPU will become the bottle but not by much at all. The only down fall is you better run your game without many background process that is also using the CPU either you overclock or not.